A Look at Overfitting in Source Estimation Problems 41 Fig. 6 The validation set of response DOFs for the overfitting study. Fig. 7 The input DOFs for the overfitting study. The spectral responses and inputs were computed as phase referenced spectra, using a force DOF as the reference and the signal processing parameters that are shown in Table 1. The responses with errors, which will be referred to as the “noised responses”, were computed by adding broadband random noise to the truth response spectra, prior to phase referencing and averaging. Note that the signal-to-noise ratio (SNR) for the noised responses was tuned so an ISE with modeling errors or response errors would result in similar levels of overfitting, as determined by the amplitude errors in the estimated sources, while still having a typical SNR for vibration measurements. The DOF averaged SNR and summed (truth and noised) response power spectral density (PSD) for all the response DOFs in the overfitting study are shown in Figure 8. This plot shows that the noised response has a good signal to noise ratio and that the noise is not dramatically contaminating the truth responses. The models and synthesized response data for the overfitting study were combined three different ways to match the different types of error that could contaminate an ISE problem. All the model/data combinations were used with both the good and bad training response DOFs, depending on the hypothesis that was being tested, and will be referred to accordingly. The model combinations were: 1. The truth model and truth response data were combined to create the baseline ISE problem 2. The truth model and noised response data were combined to create the response error ISE problem 3. The test model and truth response data were combined to create the modeling error ISE problem
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